What is the degree of homogenous `f(x,y)=e^(y/x)+tan(y/x)`?

If f(x,y)= (x-y)/(x+y) then write the degree of the homogenous function (df)/(dy) .

If tan(x+y)=e^(x+y) , then (dy)/(dx)

If tan(x+y)=e^(x+y) , then (dy)/(dx)

Which one of the following function(s) is/are homogeneous? (a) f(x,y)= (x-y)/(x^2 + y^2) (b) f(x,y)= x^(1/3)y^(-2/3)tan^-1(x/y) (c) f(x,y)=x(lnsqrt(x^2+y^2)-lny)+ye^(x/y) (d) none of these

Which one of the following function(s) is/are homogeneous? (a) f(x,y)= (x-y)/(x^2 + y^2) (b) f(x,y)= x^(1/3)y^(-2/3)tan^-1(x/y) (c) f(x,y)=x(lnsqrt(x^2+y^2)-lny)+ye^(x/y) (d) none of these

Which one of the following function(s) is/are homogeneous? (a) f(x,y)= (x-y)/(x^2 + y^2) (b) f(x,y)= x^(1/3)y^(-2/3)tan^-1(x/y) (c)f(x,y)=x(lnsqrt(x^2+y^2)-lny)+ye^(x/y) (d) none of these

Which one of the following function(s) is/are homogeneous? (a)f(x,y)=(x-y)/(x^(2)+y^(2))(b)f(x,y)=x^((1)/(3))y^(-(2)/(3))tan^(-1)((x)/(y))(c)f(x,y)=x(ln sqrt(x^(2)+y^(2))-ln y) (d) none of these

Identify the statements (s) which is/are true.f(x,y)=e^((y)/(x))+tan(y)/(x) is homogeneous of degree zero.x,ln(y)/(x)dx+(y^(2))/(x)sin^(-1)(y)/(x)dy=0 is homogeneous of degree one f(x,y)=x^(2)+sin x.cos y is not homogeneous (x^(2)+y^(2))dx-(xy^(2)-y^(3))dy=0 is a homogeneous differential equation.